PHYSICAL REVIEW B
VOLUME 56, NUMBER 10
1 SEPTEMBER 1997-II
Theoretical study of a five-coordinated silica polymorph
James Badro
Laboratoire de Sciences de la Terre (UMR 5570), Ecole Normale Supérieure de Lyon,
46 allée d’Italie F-69364 Lyon Cedex 07, France
David M. Teter
Geophysical Laboratory and Center for High Pressure Research, Carnegie Institution of Washington,
5251 Broad Branch Road, N.W., Washington, DC 20015
and Department of Materials Science and Engineering, Virginia Tech, Blacksburg, Virginia 24061
Robert T. Downs*
Geophysical Laboratory and Center for High Pressure Research, Carnegie Institution of Washington,
5251 Broad Branch Road, N.W., Washington, DC 20015
Philippe Gillet
Institut Universitaire de France, Laboratoire de Sciences de la Terre (UMR 5570), Ecole Normale Supérieure de Lyon,
46 allée d’Italie F-69364 Lyon Cedex 07, France
Russell J. Hemley
Geophysical Laboratory and Center for High Pressure Research, Carnegie Institution of Washington,
5251 Broad Branch Road, N.W., Washington, DC 20015
Jean-Louis Barrat
Departement de Physique des Materiaux (UMR 5561)-CNRS, Université Claude Bernard, 43 bd. du 11 novembre 1918,
F-69622 Villeurbanne Cedex, France
~Received 12 February 1997!
Theoretical calculations are performed to study transformations in silica as a function of nonhydrostatic
stress. Molecular-dynamics calculations reveal a crystalline-to-crystalline transition from a-quartz to a phase
with five-coordinated silicon ( VSi) at high pressure in the presence of deviatoric stress. The phase, which
appears for specific orientations of the stress tensor relative to the crystallographic axes of quartz, is a crystalline polymorph of silica with five-coordinated silicon. The structure possesses P3 2 21 space-group symmetry. First-principles calculations within the local-density approximation, as well as molecular dynamics and
energy minimization with interatomic potentials, find this phase to be mechanically and energetically stable
with respect to quartz at high pressure. The calculated x-ray diffraction pattern and vibrational properties of the
phase are reported. Upon decompression, the VSi phase reverts to a-quartz through an intermediate fourcoordinated phase and an unusual isosymmetrical phase transformation. The results suggest the importance of
application of nonhydrostatic stress conditions in the design and synthesis of novel materials.
@S0163-1829~97!04034-4#
I. INTRODUCTION
The bonding in silica gives rise to a rich variety of structures and physical properties of phases in this system as
functions of pressure and temperature. Most of the approximately 30 silica polymorphs are stable at low pressures ~e.g.,
quartz, cristobalite, and tridymite! and can be described by
various spatial arrangements of SiO4 tetrahedra.1 This fourfold coordination of silicon ( IVSi) results from strong sp 3
bonding and the large number of packing sequences is allowed by the soft, deformable, Si-O-Si linkage joining the
rather rigid SiO4 units. IVSi is the fundamental building
block of such technologically important materials as amorphous silica optical waveguides, quartz crystal oscillators,
0163-1829/97/56~10!/5797~10!/$10.00
56
and siliceous molecular sieves. It is also one of the most
common structural motifs found in minerals that make up the
Earth’s crust. At higher pressures, silicon increases its coordination number as in the high-density phase, stishovite. In
this case, the Si atoms are coordinated to six O atoms ( VISi)
to form a network of SiO6 octahedra, a configuration that
gives rise to a more ionic Si-O bond. This denser arrangement is found in many of the minerals that make up the
Earth’s mantle. Four- and six-coordinated silica polyhedra
have long been considered fundamental building blocks of
minerals, glasses, and melts relevant to the mineralogy and
geochemistry of the Earth’s interior.
The transformations among the SiO2 polymorphs have
been studied thoroughly over the years.2,3 The low-pressure
5797
© 1997 The American Physical Society
5798
JAMES BADRO et al.
transformations are not accompanied by changes in Si coordination but instead involve modifications in the manner in
which SiO4 tetrahedra are linked. The IVSi to VISi coordination changes are only observed experimentally at pressures
in excess of 8 GPa (.700 K) by the formation of stishovite.
In the recent years, other transformations have been discovered during room-temperature static compression.3 a-quartz,
the stable form at ambient conditions, undergoes a
crystalline-to-crystalline transition at 21 GPa prior to
pressure-induced amorphization.4–7 Similar transformations
have been observed for cristobalite and for the isomorphic
forms of quartz, GeO2 and AlPO4. 8–11 These transitions are
associated with the formation of tetrahedral networks, and at
higher pressure, increases in cation coordination number. Recently, it has been shown that stishovite transforms at 50
GPa to a phase having the CaCl2 structure type, which also
contains VISi. 12 Increases in Si coordination have also been
inferred from spectroscopic and diffraction measurements of
statically compressed silica glass or quartz amorphized at
room temperature.4,5,13–16
Although all of the observed stable and metastable crystalline phases of silica consist of either IVSi or VISi, there
has been great interest in the possibility of forming phases in
which silicon has fivefold coordination by oxygen ( VSi).
This species has been predicted in theoretical studies of the
effects of pressure and temperature on silicate melts and
glasses17–27 and inferred experimentally by 29Si NMR and
vibrational spectroscopy in alkali silicate liquids and
glasses.16,28–36 Silicon has also been found in fivefold coordination with oxygen in a number of organosilicon
compounds.37,38 VSi has been proposed to play a role in the
dissolution of silicates,39–41 the increased diffusivity of liquid SiO2 under pressure,18 and viscous flow processes of
other silicate melts.30–32 It has also been speculated to be an
important species in the synthesis of siliceous molecular
sieves.37,38 Thus, although VSi is suspected in high-pressure
silicates and may form part of the network of high-pressure
amorphous phases, and hypothesized in high-temperature
SiO2-rich melts or glasses, no crystalline phases of silica
containing VSi have yet been observed. The synthesis of a
crystalline phase of SiO2 entirely composed of SiO5 units
would thus be of interest from the point of view of solid-state
physics and chemistry, geophysics, and materials science.
The ability of theoretical calculations to predict the physical properties and energetics of the phases of silica has progressed significantly in recent years ~e.g., Refs. 42–45!.
First-principles electronic structure methods are now capable
of accurate predictions of phase transformations and vibrational, and elastic properties, as in the recent prediction of
the phase transition in stishovite.12 Interatomic potentials are
capable of reproducing structures, vibrational properties,
elastic properties, equations of state, and phase transitions
among the known polymorphs. Simulations with these potentials have predicted that the formation of VSi is promoted
by high pressures; for SiO2 glass these studies show that IVSi
species are gradually replaced by VSi and VISi with increasing pressure.18,19,27,40 Such simulations permit the exploration over a broad range of the effects of pressure, temperature, and deviatoric ~differential! stresses on phase stability
and physical properties. In fact, recent molecular-dynamics
simulations on a-quartz under nonhydrostatic stress found
56
evidence for a crystalline phase of SiO2 composed entirely of
SiO5 groups.27 This structure, designated here as penta-SiO2,
was discovered during a series of molecular-dynamics simulations undertaken to determine the effect of nonhydrostatic
stresses on the pressure-induced amorphization of
a-quartz.27 In these simulations, the isotropic pressure variable was replaced by the three components of the diagonal
stress tensor, and each of these variables was monitored and
controlled independently. The process allowed the system to
access configurations not otherwise found on isotropic compression of quartz.
In this paper, we present a detailed study of this transformation and this predicted phase of SiO2. As such, the paper
includes discussion of the original simulations reported as a
short letter in Ref. 27 together with the results of new calculations. The crystal structure is examined in detail using
molecular-dynamics ~MD! and energy minimization techniques with interatomic potentials, as well as first-principles
total-energy methods. These techniques are also used to determine its energetics and physical properties, including
simulated atomic positions, x-ray diffraction pattern, and vibrational density of states. We find a continuous transformation upon decompression of penta-SiO2 to a-quartz via an
intermediate crystalline phase. This is an unusual transformation, as all three crystal structures possess the same
P3 2 21 space-group symmetry. The study shows that nonhydrostatic pressures applied along carefully chosen crystallographic directions could open up a possibility for synthesizing crystalline phases that cannot otherwise be obtained by
application of hydrostatic pressure.
II. THEORETICAL METHODS
A. Molecular dynamics
The molecular-dynamics simulations were carried out in a
modified N, s ,T isobaric-isothermal canonical ensemble, in
which the stresses s xx , s y y , and s zz were monitored independently. The van Beest, Kramer, and van Santen ~BKS!
interatomic potential was used.46 The orthorhombic simulation box measured 22.326330.889317.945 Å at ambient
conditions, with the z direction parallel to the c axis of
a-quartz, and contained 1440 atoms ~480 SiO2 units!. The
system was relaxed within this orthorhombic box and the
external stress monitored using Berendsen’s scaling independently along the three directions.47 The temperature was
fixed at 300 K using Hoover’s thermostat and the equations
of motion were integrated with a time step of 1.34 fs and the
long-range Coulomb interactions were calculated using the
Ewald sum method. The maximum radius of the wave vectors sphere in reciprocal space was set to 0.273 Å 21 , and the
Ewald parameter for the real-space part of the long-range
interaction was also set to the same value. Each compression
was carried out over 50 000 steps accounting for a total compression time of 134 ps. Molecular-mechanics simulations
under P1 symmetry were also performed using the BKS
potential. The results of these calculations were very similar
to the MD results obtained with the BKS potential.
B. Local-density approximation calculations
To gain further insight into the stability and structure of
the predicted structure, first-principles total-energy calcula-
THEORETICAL STUDY OF A FIVE-COORDINATED . . .
56
5799
TABLE I. Distribution of Si and O coordination and phases produced for different s i j from the molecular-dynamics simulations at 300
K. The runs designated with a C are compression runs, while those with a D correspond to decompression runs from the specified stresses
to ambient conditions ~zero stress!.
( s xx , s y y , s zz ), GPa
~0,0,0!
~22,22,22!
~22,22,22!
~25,25,25!
~25,25,25!
~30,30,30!
~30,30,30!
~22,22,13!
~22,22,13!
~20,20,27!
~20,20,27!
~20,20,29!
~20,20,29!
C
D
C
D
C
D
C
D
C
D
C
D
IV
Si
100%
12.5%
75%
8%
69%
7%
56%
13%
97%
0%
100%
0%
99%
V
Si
0%
42%
23.5%
38.5%
26%
36.5%
36%
34%
3%
100%
0%
90%
1%
VI
Si
0%
45.5%
1.5%
53.5%
5%
56.5%
8%
53%
0%
0%
0%
10%
0%
tions were undertaken using a density-functional
framework48 within the local-density approximation ~LDA!
to electron exchange and correlation. A preconditioned
conjugate-gradient method was used to minimize the electronic degrees of freedom.49 The electronic wave functions
were expanded in a plane-wave basis set with periodic
boundary conditions. Norm-conserving pseudopotentials
constructed within the scheme developed by Troullier and
Martins50 were used. The oxygen potential was generated
using neutral 2s 2 2p 4 as the reference state with a radial cutoff of 1.45 bohr for both the s and p components of the
potential, and the radius of the nonlinear core correction was
0.57 bohr.51 The silicon potential was generated using
3s 2 3p 2 3d 0 as a reference state with a radial cutoff of 2.09
bohr for the s, p, and d components of the potential. The s
and p angular momentum channels were treated as nonlocal
components of the potential each with two radial projection
functions, and the d channel was treated as the local component of the potential. The radius of the nonlinear core correction was taken to be 1.81 bohr. Calculations performed at
various kinetic energy cutoffs indicated that a cutoff of 30
hartrees was required for satisfactory convergence of the
structural parameters. The number of special k points for the
Brillouin-zone integration was increased until the total energies had converged to below 1 m hartree/atom. For the penta
structure, we used a @442# Monkhorst-Pack grid52 giving five
special points in the irreducible Brillouin zone.
II
O
100%
34.5%
87%
30%
82%
28%
73%
32%
98%
50%
100%
45%
99%
III
O
0%
65.5%
13%
70%
18%
72%
27%
68%
2%
50%
0%
55%
1%
Recovered phase
a-quartz
Amorphous
Amorphous
Amorphous
Amorphous
Amorphous
Amorphous
Amorphous
Defective a-quartz
Penta
a-quartz
Penta1amorphous
Defective a-quartz
crystallization is complete. The principal results of the simulations are summarized in Table I. In order to further characterize the structure of the phase, a reference state was first
created by hydrostatic compression of quartz up to 20 GPa.
This compression was carried out over 134 ps integration
time. All systems were allowed to age for 13.4 ps in order to
insure that the structure was well relaxed. The system was
then uniaxially compressed ~67 ps integration time! along the
c axis up to the phase transition at 27 GPa and also relaxed
during 13.4 ps. The resulting structure of the phase is shown
in Fig. 1.
The cell parameters, atomic positions, and symmetry elements were obtained as follows. A theoretical x-raydiffraction pattern was constructed from the coordinates of
the 480 silicon and 960 oxygen atoms given in the Cartesian
system defined by the orthorhombic MD box.55 The d’s from
the 14 strongest peaks were selected and indexed.56 The cell
parameters were then refined from the full set of observable
III. RESULTS
A. Crystal structure
We begin with the results of molecular-dynamics calculations. When hydrostatic stresses are applied on the MD box
containing crystalline quartz, pressure-induced amorphization occurs at 22 GPa,27 in good agreement with other simulations ~e.g., Refs. 53 and 54!. However, different behavior is
observed when the simulations are performed in the presence
of deviatoric stresses ~nonhydrostatic pressure!. There is a
tendency to form a different crystalline phase; for a stress of
27 GPa along the c axis and 20 GPa in the a,b plane the
FIG. 1. The high-pressure phase viewed down the c axis. The
small ~dark! spheres and large ~white! spheres are the silicon and
oxygen atoms, respectively. All silicons are linked to five oxygens,
whereas half the oxygens are linked to two silicons, the other half
being linked to three silicon atoms. The unit cell is shown in the
center.
5800
56
JAMES BADRO et al.
FIG. 2. Calculated powder x-ray-diffraction pattern of the SiO2
penta for the relaxed structure ( P516 GPa).
peak positions. The position and orientation of the unit cell
within the orthorhombic box was then determined by choosing the centermost Si atom as the origin and finding the other
Si atoms that were related to it by translational lattice symmetry, with the unit-cell distances thus defining a transformation matrix from the Cartesian system of the orthorhombic box to the direct crystal space. All the atoms were then
projected into the unit cell. The latter contained 18 atoms and
this produced a distribution of 80 atoms at each of the sites.
The position for each atom in the unit cell was chosen to be
the mean of this distribution. The positions of the atoms in
the unit cell were then analyzed to determine its possible
symmetry operations.57 Prototype asymmetric unit positions
were arbitrarily chosen and each atom was then mapped onto
its corresponding prototype, producing three distributions of
six atoms each. The average of these distributions gave the
positions assigned to the asymmetric unit. The d spacings of
the 14 most intense peaks were indexed with trigonal symmetry. Every peak could then be indexed under this symmetry with a very high figure of merit of 214.58 The space group
was found to be P3 2 21 (No.154) within a tolerance of
0.0038 Å. This is identical to the space group of a-quartz.
The cell parameters were then refined by energy minimization with both the interatomic potential and LDA methods.
The same space group was found when the structure was
relaxed under P1 symmetry with both methods, and the
structural parameters are in good agreement. The resulting
powder x-ray-diffraction pattern for the optimized structure
is shown in Fig. 2.
B. Local structure and coordination
The structure consists of silicon in fivefold coordination
by oxygen, with oxygen atoms in both two- and threefold
coordination with silicon. The SiO5 pentahedra form a distorted square pyramid linked together as edge-sharing dimers
to form a three-dimensional network. A detail of the distorted square pyramidal pentahedron is shown in Fig. 3, and
the structural parameters at a reference hydrostatic pressure
of 16 GPa are given in Table II. The mean Si-O distance
within a pentahedron ~1.703 Å from LDA; 1.680 Å from
BKS at this pressure! falls between that typically observed in
FIG. 3. Detail of the SiO5 polyhedron showing the labeling of
the atoms and bond lengths calculated by LDA ( P516 GPa).
SiO4 ~1.61 Å! and SiO6 polyhedra ~1.79 Å!.3 According to
the LDA result, four of the five Si-O bond lengths within the
SiO5 units range from 1.617 to 1.728 Å, whereas the bond
between the Si and the apical O is longer value of 1.869 Å.
This result is also reflected in the Si-O radial distribution
function ~RDF!, which is compared to those calculated for
a-quartz and stishovite in Fig. 4. These were computed from
the simulations with the BKS potential by averaging over
10 000 configurations, and the local atomic coordination
number was determined by integrating all atomic distances
lower than the first minimum in the RDF. The large anisotropy in bond lengths, which is not observed in SiO4 or SiO6
polyhedra, seems to be characteristic of the SiO5 units. Also,
two O-Si-O angles are close to 90° ~97 and 94°! while the
two others are larger: 104 and 112°. Notably, the calculated
distortion of the pentahedra is similar to that recently
TABLE II. Structural parameters of penta-SiO2 ( P516 GPa)
~space group P3 2 21!.
a
c
Si(x,y,z)
O(1)(x,y,z)
O(2)(x,y,z)
Si-O~1!
Si-O~2!
Si-O~3!
Si-O~4!
Si-O~5!
O~1!-Si-O~2!
O~1!-Si-O~3!
O~1!-Si-O~4!
O~1!-Si-O~5!
O~2!-Si-O~3!
O~2!-Si-O~4!
O~2!-Si-O~5!
O~3!-Si-O~4!
O~3!-Si-O~5!
O~4!-Si-O~5!
LDA
BKS Potential
4.414 Å
9.358 Å
0.5126 0.3224 0.2204
0.4839 0.0761 0.0537
0.8253 0.6686 0.1439
1.869 Å
1.728 Å
1.674 Å
1.626 Å
1.617 Å
168.2°
76.3
87.6
94.6
95.9
93.7
96.3
142.4
108.9
106.1
4.462 Å
9.123 Å
0.5045 0.3087 0.2214
0.4776 0.0775 0.0526
0.8200 0.6431 0.1425
1.824 Å
1.714 Å
1.636 Å
1.620 Å
1.605 Å
169.2°
76.5
85.8
94.6
96.1
91.8
99.1
140.8
112.7
103.7
56
THEORETICAL STUDY OF A FIVE-COORDINATED . . .
5801
FIG. 4. Radial distribution function ~RDF! for silicon and oxygen ~16 GPa and 300 K!. The reported first-neighbor distances for
penta-SiO2 lie between that for quartz and stishovite. The computed
average Si-O bond lengths are 1.60, 1.68, and 1.75 Å, for a-quartz,
penta-SiO2, and stishovite, respectively.
observed for a calcium silicate phase consisting of VSi. 59,60
The Si-O bond lengths determined in that study ~measured at
zero pressure! are 1.671, 1.682, 1.696, 1.781, and 1.824 Å
with an average value of 1.731 Å.
C. Band structure
The electronic band structures for both penta and a-quartz
were also calculated. Figure 5 shows the band structures and
associated total density of states ~TDOS! for the two phases
along high-symmetry directions of the Brillouin zone of the
hexagonal unit cell at a common pressure of 16 GPa. The
zero of the energy scale corresponds to the valence band
maximum. The penta phase is an insulator with a direct gap
calculated by LDA of 4.9 eV at G, whereas a-quartz has an
indirect gap calculated to be 6.4 eV ~valence band maximum
at K and a conduction band minimum at G!.
At ambient pressure, the valence-band structure of
a-quartz is separated into three distinct regions ~for a review,
see Ref. 42!. The lowest is composed mainly of O 2s states
with a small contribution from Si 3s and 3p states. The
middle is composed of O 2 p and Si 3s and 3p states with a
small contribution from the Si 3d states. The states in this
region contribute principally to the Si-O bonding. The top of
the valence band is primarily composed of O 2 p nonbonding
states, with a very small contribution from Si 3 p and 3d. At
16 GPa however, the middle ~bonding! and top ~nonbonding!
regions have merged @Figs. 5~b! and 5~d!#. This result is in
agreement with the previous work on a-quartz by Binggeli
et al.61 and Di Pomponio and Continenza.62 It has been suggested that this rehybridization can favor Si-O bonding with
the silicon in higher coordination.61,62 The band structure and
TDOS @Figs. 5~a! and 5~c!# of penta-SiO2 reveal significantly
more mixing of these regions than occurs in a-quartz, but
less than that found for stishovite.63
D. Vibrational density of states
The vibrational densities of states ~VDOS! of the penta
phase is of interest because it contains the signature of the
FIG. 5. Band structures: ~a! penta-SiO2, ~b! a-quartz; total density of states: ~c! penta-SiO2, ~d! a-quartz. The calculations were
performed at a common pressure of 16 GPa.
vibrations related to SiO5 units which could serve to identify
these units by neutron inelastic-scattering, infrared, or Raman spectroscopy. The VDOS of quartz and penta-SiO2 were
computed by MD at 16 GPa ~see Fig. 6!. The VDOS were
calculated from the Fourier transform of the mass weighted
JAMES BADRO et al.
5802
FIG. 6. Vibrational density of state of the penta phase and
a-quartz calculated using the power spectrum of the velocity autocorrelation function ~P516 GPa; T5300 K!.
power spectrum of the velocity autocorrelation functions
~VAF’s!,64 computed in the (N,V,E) microcanonical ensemble. The VAF’s were calculated for runs up to 2.68 ps
and averaged over 2000 configurations after a 13.4 ps constant energy run. They have been smoothed by a Gaussian
distribution of width 10 cm21 to be comparable to the resolution of typical inelastic neutron-scattering experiments.
There are a number of important differences. A clear gap in
the VDOS of quartz exists between the lower frequency
modes ~up to 900 cm21! and those at 1100– 1350 cm21. This
gap is present in the measured Raman and IR spectra of
quartz ~and other SiO2 polymorphs consisting of SiO4
units!,65 but it is less pronounced in the VDOS predicted for
the new phase. The higher frequency group of modes corresponds to asymmetrical Si-O stretching motions within the
SiO4 units. The corresponding modes in the penta phase involve similar vibrations of SiO5 groups, but they are shifted
toward lower wave numbers (950– 1250 cm21). The lower
wave numbers reflects the longer mean Si-O bond length,
similar to the downward frequency shift and longer bond
lengths documented for the SiO6 octahedra ~e.g., in
stishovite4,16!. The broadening of this group of modes in the
penta phase results from the existence of different bond
lengths within the SiO5 groups in comparison to the SiO4
tetrahedra of quartz. This difference in VDOS between
quartz and penta-SiO2 thus should serve as a signature of the
fivefold coordination of Si, because these features of the
VDOS should be reflected in the Raman and IR spectra.65
Differences between quartz and the penta phase are also observed below 900 cm21, but they are less diagnostic than
those observed at higher wave numbers.
56
FIG. 7. Energy as a function of volume calculated by LDA. The
structure is fully optimized at each volume.
phases are shown in Fig. 7, where the calculated points are fit
to a Birch-Murnaghan equation of state.66 The penta phase is
metastable with respect to quartz above a critical volume of
15.78 cm3/mole (3.80 g/cm3). This result is in agreement
with the MD calculations which show that the quartz-topenta transition takes place when quartz reaches a critical
volume of 17.29 cm3/mol (3.47 g/cm3). The molar volume
of the penta phase obtained by MD (15.67 cm3/mol) at the
transition pressure is very close to that obtained by LDA.
The P-V equations of state calculated from the energyvolume curves are shown in Fig. 8. The results are close to
those determined from the BKS potential. We also compare
both the LDA and BKS results for quartz and stishovite, as
well as experimental results for both phases.67–74 Both the
molar volume and compressibility of penta-SiO2 are intermediate between those of a-quartz and stishovite at all pressures. The good agreement between theory and experiment
for quartz and stishovite, also shown in previous studies using both LDA ~Ref. 75! and the BKS potential,53,76 supports
the reliability of the prediction for the metastable phase.
E. Stability and equation of state
A series of calculations were performed to examine the
stability of the phases as a function of compression and decompression. The LDA calculations confirm the transition
from quartz to the penta phase obtained in the MD simulations. The energy-volume curves calculated by LDA for the
FIG. 8. The pressure-volume equation of state for penta-SiO2,
a-quartz, and stishovite. The solid and dashed lines are the LDA
and the interatomic potential results ~static lattice!. The symbols are
experimental room-temperature static compression data for
a-quartz ~Refs. 67–71! and stishovite ~Refs. 72–74!.
56
THEORETICAL STUDY OF A FIVE-COORDINATED . . .
5803
FIG. 9. Comparison of the crystal structures of ~a! penta-SiO2,
~b! the intermediate phase, and ~b! a-quartz. The atoms are numbered in Fig. 3.
F. Phase transformations
Both the MD and LDA calculations provide insights on
the transitions on compression or decompression. MD simulations at the pressure of formation predict that the pentaSiO2 withstands temperatures up to 1500 K without exhibiting any phase transitions. Upon further uniaxial pressurization at room temperature, the penta phase undergoes partial
amorphization for a stress along the c direction 2 GPa above
that at which it is formed. In contrast with the solid-state
amorphization of quartz, which yields a mixture of IVSi,
V
Si, and VISi in simulations,27 this amorphous material contains only silicon atoms in five- and sixfold coordination.
When decompressed, this amorphous phase undergoes a partially reversible transition to a defective quartzlike material
at 10 GPa ~Table I!.
Both the LDA and BKS calculations indicate that the
penta phase is energetically stable with respect to quartz below a critical volume. MD simulations carried out on decompression predict that penta-SiO2 reverts to a-quartz at a pressure of 2 GPa when the decompression path is identical to
that followed on compression ~i.e., the excess uniaxial stress
is first released from 27 GPa down to 20 GPa and the hydrostatic environment is maintained during further decompression!. Both the LDA calculations and molecular mechanics
methods show that penta-SiO2 transforms to a transient intermediate structure before fully relaxing to a-quartz. This
intermediate phase, which also has IVSi, is therefore an unstable phase in the system. The structures are compared in
Fig. 9.
The mechanism of the transformation was examined in
detail. Because of the bond breaking along the transformation path and the existence of Si-O bonds outside the range
of parametrization of the BKS potential, the LDA results are
considered more reliable. The results show that during decompression the SiO5 polyhedra first expand and distort, as
shown in Fig. 10. Both the Si-O bond lengths and Si-O-Si
angles increase for the two-coordinated oxygens. The transformation to the intermediate structure occurs when the Si-O
bond of the apical oxygen breaks ~a distance of approximately 2.0 Å!. At this point, the four remaining Si-O distances rapidly decrease, transforming the SiO5 pentahedra
into distorted SiO4 tetrahedra. These tetrahedra then rotate to
form the a-quartz structure to reduce the strain.
IV. DISCUSSION
Despite the large number of high-pressure studies of
quartz in recent years, the effects of nonhydrostatic stresses
FIG. 10. Structural variations in the penta phase as a function of
volume during decompression. Si-O-Si bond angles ~top!. Si-O
bond distances ~bottom!.
on its phase transitions, structures, and dynamics, are not
fully understood. The present calculations indicate that specific nonhydrostatic stress conditions can radically alter the
compression behavior of a-quartz. Lattice-dynamics calculations performed with the BKS potential predict a pressureinduced phonon softening in hydrostatically compressed
quartz; complete softening is calculated to occur at 21 GPa,
prior to the onset of a mechanical instability.77 Another study
using lattice dynamics calculations has predicted a dynamical instability at 18.5 GPa in the @ 1/3,1/3,0 # direction of the
Brillouin zone.78 This transition pressure is close to that of
the experimentally reported crystalline-crystalline phase
transition documented in high-pressure hydrostatic experiments of quartz.7 The present study strongly suggests that
when quartz is compressed in a nonhydrostatic manner with
the stress along c greater than that along a and b, this instability is postponed to higher pressures. The resulting strain
allows the silicon atoms to experience a different oxygen
environment than would normally be encountered under hydrostatic conditions. In the case of a stress tensor with s xx
520 GPa, s y y 520 GPa, s zz 527 GPa, a low-energy pathway is created between quartz to the penta structure, thereby
facilitating the transformation to the penta phase.
As discussed above, the VSi phase is produced by application of deviatoric stresses but is stable mechanically and
energetically ~e.g., with respect to quartz! at fixed hydrostatic
5804
JAMES BADRO et al.
56
pressure. An unusual sequence of transformations occurs as a
function of decreasing hydrostatic pressure. There appears to
be a continuous, low-energy path between the penta, the intermediate phase, and a-quartz transition. During the transformation, the coordination number of the silicon changes
from five to four, and several of the oxygens change from
three- to twofold. Notably, this takes place with no change in
P3 2 21 symmetry, even when the symmetry constraints are
relaxed ~i.e., calculations under P1 symmetry!. Christy79 has
denoted this class of phase transformations, in which no
change of space group occurs, as type 0. Such isosymmetric
phase transitions have been shown to occur in feldspars,
pyroxenes,80 and nonlinear optical materials ~e.g.,
KTiPO4!.81
As the two phases identified here have not been observed
experimentally, it is useful to examine the accuracy of the
theoretical techniques used in the calculations. Numerous
studies have tested the reliability of the BKS potential, which
is similar to the earlier potential of Tsuneyuki et al.82 but is
more accurate for a number of physical properties of crystalline polymorphs ~e.g., Ref. 76!. As illustrated in Fig. 8, both
the LDA and interatomic potential calculations are able to
accurately reproduce the experimental compression behavior
of both a-quartz67–71 and stishovite.72–74 Despite the success
of the model potential, such methods are considered inherently approximate, and indeed problematic for processes
such as bond breaking and making, so it is useful to consider
more accurate methods. We believe that the LDA calculations are more reliable for predicting the structural properties
of penta-SiO2 as well as the decompression behavior. It has
been reported recently that generalized gradient approximations ~GGA! to the exchange and correlation energy are required to describe accurately the energy difference between
a-quartz and stishovite.83 While the GGA gives a more correct energy difference, it appears to do so at the expense of
accuracy of the structural parameters. Our interest in the
structural parameters of the five-coordinated silica phase
therefore justifies the use of the LDA. Additional studies
using the GGA and other extensions of LDA would be valuable.
It is useful to examine measurable signatures of the structure such as the diffraction pattern and vibrational properties
to aid in the possible experimental identification of the penta
phase. This is of interest because of the possibility of
whether such material may have been formed in small quantities during previous high-pressure experiments. Studies of
metastable transitions in silica, and quartz in particular, produce heterogeneous samples, with small amounts of crystalline ~or partially crystalline material! mixed with material
having disorder ranging from extensive twinning to com-
pletely amorphous.6,7 Both vibrational and diffraction measurements yield broadbands. Deviatoric stresses are present
to some degree in most experimental studies: Under such
conditions, local stresses within the heterogeneous sample
are expected to be significant, even if the sample assemblage
is in a hydrostatic environment, because of local
grain-grain-contacts.3 We anticipate that the calculated
VDOS may be useful for spectroscopic identification of either the penta phase or the presence of SiO5 units in crystalline or amorphous silicates. It may useful to compare both
predicted diffraction peaks and vibrational properties for
penta-SiO2 with existing and future measurements on such
compressed metastable silica samples. As discussed above, a
high-pressure phase of CaSi2O5 consisting of VSi has recently been synthesized and characterized.59,60 The silicon
and oxygen form distorted square pyramidal pentahedra, and
the structural parameters, including the Si-O bond lengths,
are similar to those predicted for the pure SiO2 phase.
In conclusion, this study shows that it is possible to control transformation pathways of quartz to new polymorphs,
and as such, it illustrates the continued richness of the SiO2
system. It appears possible to use such methods to tune pathways as functions of hydrostatic and nonhydrostatic stress to
find phases in other chemical systems. While variable stress
has long been used in the synthesis of thin films through the
control of lattice mismatch between the substrate and film,
we suggest it is possible to synthesize new materials by using deviatoric stress to control the pathway of the phase
transformation. This is of added interest in view of recently
developed experimental techniques for controlling and directly measuring the three-dimensional distribution of stress
and strain in samples under high confining pressures ~e.g., in
diamond-anvil cells!.84,85 Such techniques may allow synthesis of crystalline phases that cannot be obtained by application of hydrostatic pressure, and therefore could be important
for solid-state engineering and creation of new materials.
*Present address: Department of Geosciences, University of Ari-
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ACKNOWLEDGMENTS
We are grateful to C. T. Prewitt and R. E. Cohen for
comments on the manuscript and useful discussions. We
thank the Pôle Scientifique de Modélisation Numérique
~ENS-Lyon!, the Cornell Materials Science Computing Center, and the Virginia Tech Computing Center for use of
CONVEX SPP 1000, IBM RS/6000 and SP2 computing resources, respectively. D.M.T. thanks Doug Allan of Corning,
Inc. for valuable contributions. This work was partially supported by the NSF. The Center for High Pressure Research is
an NSF Science and Technology Center.
56
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